Physical Sciences and Mathematics Commons^™

3-Manifold Perspective On Surface Homeomorphisms For Surfaces With Very Negative Euler Characteristic, Michael Harris

Graduate Theses and Dissertations

The goal of this paper is to show for a compact triangulated 3-manifold M with boundary which fibers over the circle that whenever F is a fiber with sufficiently negative Euler characteristic the monodromymaps an essential simple closed curve or an essential simple arc in F to be disjoint from its image (possibly after isotopy). This is shown by applying the theorem of Ichihara, Kobayashi, and Rieck in [10] to the double of M to get a pair of pants. We then find an equivariant pair of pants and use it to find an essential simple closed curve or an …

On Compactness And Closed-Rangeness Of Composition Operators, Arnab Dutta

Graduate Theses and Dissertations

Let $\phi$ be an analytic self-map of the unit disk $\mathbb{D}:=\{z:\lvert z\rvert

The Maximal Thurston-Bennequin Number On Grid Number N Diagrams, Emily Goins Thomas

Graduate Theses and Dissertations

We will prove an upper bound for the Thurston-Bennequin number of Legendrian knots and links on a rectangular grid with arc index n.

TB(n)=CR(n)-[n/2]

In order to prove the bound, we will separate our work for when n is even and when n is odd. After we prove the upper bound, we will show that there are unique knots and links on each grid which achieve the upper bound. When n is even, torus links achieve the maximum, and when n is odd, torus knots achieve the maximum.

Good Stein Neighborhood Bases For Nonsmooth Pseudoconvex Domains, Chizuko Iwaki

Graduate Theses and Dissertations

In 1979, Dufresnoy showed that the existence of a good Stein neighborhood base for Ω ⊂ℂⁿ implies that one can solve the inhomogeneous Cauchy-Riemann equations in C^∞(Ω̄), even if the boundary of Ω is only Lipschitz. In my thesis, I will show sufficient conditions for the existence of a good Stein neighborhood base on a Lipschitz domain satisfying Property (P).

Isometries Of Besov Type Spaces Among Composition Operators, Melissa Ann Shabazz

Graduate Theses and Dissertations

Let Bp,alpha for p >1 and alpha >1 be the Besov type space of holomorphic functions on the unit disk D. Given Phi, a holomorphic self map of D, we show the composition operator CPhi is an isometry on Bp,alpha if and only if the weighted composition operator WPhiPhi, is an isometry on the weighted Bergman space Ap,alpha. We then characterize isometries among composition operators in Bp,alpha in terms of their Nevanlinna type counting function. Finally, we find that the only isometries among composition operators on Bp,alpha, except on B 2,0, are induced by rotations. This extends known results by …

Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey

Doctoral Dissertations

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do not routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together …

A Mathematical Model And Numerical Method For Thermoelectric Dna Sequencing, Liwei Shi

Doctoral Dissertations

DNA sequencing is the process of determining the precise order of nucleotide bases, adenine, guanine, cytosine, and thymine within a DNA molecule. It includes any method or technology that is used to determine the order of the four bases in a strand of DNA. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. Thermoelectric DNA sequencing is a novel method to sequence DNA by measuring the heat that is released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a growing DNA strand. The thermoelectric device for this project is composed of four parts: …